Mathematical analyses and models are powerful tools for understanding physiology and effectively using research resources. Mathematical analyses enable extraction of additional information from data sets. Mathematical modeling forces explicit definition of the variables involved, their response to stimuli and their interactions, and frequently clarifies areas of fruitful future experimentation and intervention. For this proposal, the Analytic Core helped develop the experimental protocols. Each of the experimental Projects will do primary and secondary analyses of their data sets. The Analytic Core will extend their work by providing more detailed mathematical analyses and modeling by using data from multiple projects, as well as by developing and applying more sophisticated mathematical techniques and modeling tools. The development of new mathematical analyses and models of biological systems is a complicated process, ideally involving understanding of the biology and mathematics and interactions of the experimenters and mathematicians. An Analytic Core within a Program Project Grant is an ideal situation for such work. The Specific Aims are to: (1) To develop and quantify the relative merits of different measures of short-term (within a bedrest episode) and long term (across bedrest episodes) sleep drive (or "pressure") within a bedrest episode and to quantify how these measures of sleep drive are affected by circadian phase, time within a bedrest episode, chronic sleep restriction (CSR) and age;(2) To apply these analyses to data on human and rat sleep and wake bouts and to quantify the similarities and differences between human and rodent models;(3) To develop and quantify the relative merits of different measures of short-term and longer-term sleep drive on subjective alertness and objective neurobehavioral performance within a wake episode and to quantify how these measures of wake-time alertness and performance vary with circadian phase, time within a wake episode, CSR, and age.;(4) To apply these analyses and analyses from Core C (Polysomnographic Core) to quantify the inter-relationships of sleep drive and metabolic changes during CSR;and (5) To continue development of a mathematical model of the human circadian pacemaker and its effects on sleep, subjective alertness and objective neurobehavioral performance. The Analytic Core will develop and test mathematical analyses and modeling applicable to many projects.